Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.     

基于能量原理确定系泊碰撞载荷的有限元法

准确地确定出船舶系泊时的撞击载荷, 对船舶及海洋平台的强度研究都是极其重要的. 提出了通过能量原理和有限元分析确定系泊撞击载荷的方法. 碰撞时, 动能和变形能满足能量守恒, 动能是包括附连水质量在内的船体总动能, 此动能在撞击时转化为变形能, 根据变形能与载荷的关系, 求出碰撞载荷. 通过具有碰撞载荷理论解的梁的验证, 表明该方法是完全可行的. 为实际工程提供了确定护舷撞击力的理论依据和计算方法.     

舰船捷联惯导传递对准仿真验证系统设计

为解决船用捷联惯导系统传递对准仿真中载体机动方式与实际差别较大的问题,提出了基于舰船空间运动的传递对准精度考核的仿真验证系统,提高载体机动方式仿真逼真度。仿真验证系统通过舰船空间运动建模,提供接近真实运动环境的空间运动参数;通过设计空间变换算法,实现了空间运动参数与主惯导惯性器件模拟输入的转化;通过杆臂及挠曲变形计算,实现了子惯导惯性器件模拟输入的转化;文中给出了各模块的算法及解算流程。速度+姿态传递对准算法仿真验证结果为10 s内水平失准角精度优于0.02;方位失准角精度优于0.05。仿真验证试验结果表明了该方案的可行性和实用性,该方案为其他领域的传递对准方案分析及验证提供了有效的参考依据。     

Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes

We present a parallel multigrid solver on locally refined meshes for solving very complex three‐dimensional flow problems. Besides describing the parallel implementation in detail, we prove the smoothing property of the suggested iteration for a simple model problem. For demonstration of the efficiency and feasibility of the solver, we show a chemically reactive flow simulation for a Methane burner using detailed chemical reaction modeling. Further, we give the results of an ocean flow simulation. All described methods are implemented in the finite element toolbox Gascoigne. Copyright © 2010 John Wiley & Sons, Ltd.     

弹性壳结构静力与动力分析的光滑粒子法

本文通过采用移动最小二乘函数作为近似函数 和完全拉格朗日方程作为近似方程来改善光滑粒子法的稳定性和数值精度; 在此基础上, 提出了壳结构静力分析的光滑粒子法, 并完善了壳结构动力分析方法; 最后, 采用国际公认的壳结构的标准测试模型对静力和动力问题分别进行了验证, 所得结果与已有数据吻合良好, 证明了本文数值模型的有效性和可靠性, 为光滑粒子法进一步在裂纹、破碎等非线性壳结构中的应用提供参考. 关键词： 弹性壳 静力与动力分析 光滑粒子法 完备性和稳定性     

光滑粒子流体动力学方法固壁处理的一种新型排斥力模型

与传统网格法相比, 光滑粒子流体动力学方法不能直接施加壁面边界条件, 这就限制了该方法在工程中的应用.为此, 本文基于Galerkin加权余量法并结合传统排斥力方法, 推导出一种新的排斥力公式来施加壁面边界条件.该方法不含未知参数, 能在不减小边界粒子尺寸的情形下有效地防止流体粒子穿透壁面, 同时可避免邻近边界的流体粒子的速度及压力振荡. 分别通过静止液柱算例、液柱坍塌算例、容器中液体静止算例及溃坝算 例来验证本文方法的有效性, 并与传统边界处理方法进行对比, 结果表明: 本文方法克服了传统方法存在的缺陷, 是一种有效的固壁边界处理方法. 关键词： 光滑粒子流体动力学法 固壁边界 排斥力 加权余量法     

Thin-Film Flow Influenced by Thermal Noise

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely on a long-wave-approximation and Fokker–Planck-type arguments. We formulate a discretization method and give first numerical evidence for our conjecture that thermal fluctuations are capable of accelerating film rupture and that discrepancies with respect to time-scales between physical experiments and deterministic numerical simulations can be resolved by taking noise effects into account.     

General Theory of Acoustic Wave Propagation in Liquids and Gases

We study the propagation of small-amplitude acoustic waves in liquids and gases and use the hydrodynamic equations to obtain an exact dispersion equation. This equation in dimensionless variables contains only two material constants p and q. We solve the dispersion equation, obtaining an exact solution that holds for all values of the parameters and all frequencies up to hypersonic, and thus analytically establish exactly how the speed of sound c, the wave vector k, and the damping factor x depend on the frequency ω and the dimensionless material constants p and q. Studying the behavior of the solution in the sonic and ultrasonic frequency bands for ω < 10⁷ sec^-1 results in an expression for the damping factor, which differs from the Kirchhoff formula. The speed of sound c and the wave vector k are shown to have finite nonzero values for all hypersonic frequencies. At the same time, there exists a certain maximum frequency value, ω_max ≈ 10¹¹-10¹² sec^-1, at which the damping factor x is zero. This frequency determines the boundary of the applicability domain for the hydrodynamic equations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 340–352, February, 2006.     

A diffusion equation in transparent media

In this paper we study the homogeneous relativistic heat equation (HRHE) obtained as asymptotic limit of the so-called relativistic heat equation (RHE) when the kinematic viscosity ν → ∞. These equations were introduced in the theory of radiation hydrodynamics to guarantee a bounded speed of propagation of radiating energy. We shall prove that this is indeed true, and we shall construct some explicit solutions of the HRHE exhibiting fronts propagating at light speed.     

浅水域中多船编队航行时的船波干涉

以Green-Naghdi(GN)方程为基础,采用波动方程和运动网格的有限元法研究多船在浅水域中集体航行时的波浪干涉特性。把运动船舶对水面的扰动作为移动压强直接加在GN方程里,以描述运动船体和水面的相互作用。GN方程合理地考虑非线性和频率散射对浅水船波的影响。以Series60 CB=0.6船体为算例,给出两船并行、前后跟随、三船品字形编队航行时的波浪干涉图形,波浪阻力及侧向力的数值分析结果。计算结果表明:1)当两船并行时,两船承受侧向吸引力,同时波浪阻力稍有增加。2)当两船前后跟随时,两船的波浪阻力都减小。3)当三船品字形航行时,前船的阻力减小,后船的阻力增加,同时后面两船的吸力减小。